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HO                      ANALYTICAL MECHANICS
pound-mass or one pound-weight?'7* The difficulty is due to the fact that the common methods for comparing the masses of bodies make use of their weights.
There are two general methods by which masses may be compared, both of which are based upon the force equation. Let Fi and F2 be the resultant forces acting upon two bodies having masses mi and m2, and /i and /2 be the accelerations produced. Then the force equation gives
_
and
Fz = m2/2, ml _ Fi
(1) If the forces are of such magnitudes that the accelerations are equal then the masses are proportional to the forces; for when/i = /2, the last equation becomes
This gives us a method of comparing masses, of which the common method of weighing is the most important example.
* This question may be answered in the following manner. " The fruit which you get has a mass of 1 pd. (about 453.6 gm.) and which weighs 1 Ib. (about 4.45 X 106 dynes) . If the fruit could be shipped to the moon during the passage the weight would diminish down to nothing and then increase to about one-sixth of a pound. The zero weight would be reached at a point about nine-tenths of the way over. Up to that position the weight would be with respect to the earth, that is, the fruit would be attracted towards the earth; but from there on the weight would be with respect to the moon. The mass of the fruit, however, would be the same on the earth, during the passage, and on the moon. It would be the same with respect to the moon as it is with respect to the earth. Mass is an intrinsic property of matter, therefore it does not change. Weight is the result of gravitational attraction; consequently it depends upon, (a) the body which is attracted, (b) the bodies which attract it, and (c) the position of the former relative to the latter. It is evident therefore that when a body is moved relative to the earth its weight changes."